# 5.6 Break - Even Point for a single product

#### Finding the break-even point

A company breaks even for a given period when sales revenue and costs charged to that period are equal. Thus, the break-even point is that level of operations at which a company realizes no net income or loss.

A company may express a break-even point in dollars of sales revenue or number of units produced or sold. No matter how a company expresses its break-even point, it is still the point of zero income or loss. To illustrate the calculation of a break-even point watch the following video and then we will work with the previous company, Video Productions.

Before we can begin, we need two things from the previous page:  Contribution Margin per unit and Contribution Margin RATIO.  These formulas are:

 Contribution Margin per unit = Sales Price - Variable Cost per Unit

 Contribution Margin Ratio = Contribution margin (Sales - Variable Cost) Sales
Break-even in units

Recall that Video Productions produces DVDs selling for $20 per unit. Fixed costs per period total$40,000, while variable cost is $12 per unit. We compute the break-even point in units as:  BE Units = Fixed Costs Contribution Margin per unit Video Productions contribution margin per unit is$ 8 ($20 selling price per unit -$ 12 variable cost per unit). The break even point in units would be calculated as:

 BE Units = Fixed Costs $40,000 = 5,000 units Contribution Margin per unit$8
The result tells us that Video Productions breaks even at a volume of 5,000 units per month. We can prove that to be true by computing the revenue and total costs at a volume of 5,000 units. Revenue = (5,000 units X  $20 sales price per unit)$100,000. Total costs = $100,000 ($40,000 fixed costs + $60,000 variable costs calculated as$12 per unit X 5,000 units).

Look at the cost-volume-profit chart and note that the revenue and total cost lines cross at 5,000 units—the break-even point. Video Productions has net income at volumes greater than 5,000, but it has losses at volumes less than 5,000 units.

Break-even in sales dollars Companies frequently think of volume in sales dollars instead of units. For a company such as GM that makes Cadillacs and certain small components, it makes no sense to think of a break-even point in units. GM breaks even in sales dollars.

The formula to compute the break-even point in sales dollars looks a lot like the formula to compute the break-even in units, except we divide fixed costs by the contribution margin ratio instead of the contribution margin per unit.

The contribution margin ratio expresses the contribution margin as a percentage of sales. To calculate this ratio, divide the contribution margin per unit by the selling price per unit, or total contribution margin by total revenues. Video Production's contribution margin ratio is:

 Contribution Margin Ratio = Contribution margin $8 = 0.4 or 40% Sales$20
Or, referring to the income statement in which Video Productions had a total contribution margin of $48,000 on revenues of$ 120,000, we compute the contribution margin ratio as contribution margin $48,000 / Revenues$120,000 = 0.40 or 40%.

That is, for each dollar of sales, there is a $0.40 left over after variable costs to contribute to covering fixed costs and generating net income. Using this contribution margin ratio, we calculate Video Production's break-even point in sales dollars as:  BE in Sales Dollars = Fixed Costs$40,000 = $100,000 Contribution Margin RATIO 0.40 The break-even volume of sales is$ 100,000 (can also be calculated as break even point in units 5,000 units x sales price $20 per unit). At this level of sales, fixed costs plus variable costs equal sales revenue, as shown here:  Revenue$ 100,000 (5,000 units x $20 per unit) Less: variable costs 60,000 (5,000 units x$12 per unit) Contribution margin 40,000 (100,000 - 60,000) Less: Fixed costs 40,000 Net Income $0 Margin of Safety If a company's current sales are more than its break-even point, it has a margin of safety equal to current sales minus break-even sales. The margin of safety is the amount by which sales can decrease before the company incurs a loss. For example, assume Video Productions currently has sales of$120,000 and its break-even sales are $100,000. The margin of safety is$ 20,000, computed as follows:

Margin of safety = Current sales – Break even sales

Margin of safety = $120,000 -$ 100,000 = $20,000 Sometimes people express the margin of safety as a percentage, called the margin of safety rate or just margin of safety percentage. The margin of safety rate is equal to  Margin of Safety Percent = Current Sales - Break even Sales Current Sales Using the data just presented, we compute the margin of safety rate is$20,000 / 120,000 = 16.67 %

This means that sales volume could drop by 16.67 percent before the company would incur a loss.

Targeted Profit or Income

You can also use this same type of analysis to determine how many sales units or sales dollars you would need to make a specific profit (very helpful!).  The good news is you have already learned the basic formula, we are just changing it slightly.  The formulas we will need are:

 Units at Target Profit = Fixed Costs + Target Income Contribution Margin per unit

 Sales Dollars for Target Profit = Fixed Costs + Target Income Contribution Margin RATIO
These look familiar (or they should!).  These are the same formulas we used for break even analysis but this time we have added target income.  If you think about it, it IS the same formula because at break even our target income is ZERO.

Let's look at another example. The management of a major airline wishes to know how many seats must be sold on Flight 529 to make $8,000 in profit. To solve this problem, management must identify and separate costs into fixed and variable categories. The fixed costs of Flight 529 are the same regardless of the number of seats filled. Fixed costs include the fuel required to fly the plane and crew (with no passengers) to its destination; depreciation on the plane used on the flight; and salaries of required crew members, gate attendants, and maintenance and refueling personnel. Fixed costs are$12,000.

The variable costs vary directly with the number of passengers. Variable costs include snacks and beverages provided to passengers, baggage handling costs, and the cost of the additional fuel required to fly the plane with passengers to its destination. Management would express each variable cost on a per passenger basis.  Variable costs are $25 per passenger. Tickets are sold for$125 each. The contribution margin is $100 ($125 sales - $25 variable) and the contribution margin ratio is 80% ($100 contribution margin /$125 sales). We can calculate the units and sales dollar required to make$8,000 in profit by:

 Units at Target Profit = Fixed Costs + Target Income = 12,000 + 8,000 = $20,000 = 200 tickets Contribution Margin per unit$100 $100 The sales dollars required could be calculated as break even units of 200 tickets x$125 sales price per ticket = $25,000 or by using the following formula:  Sales Dollars for Target Profit = Fixed Costs + Target Income = 12,000 + 8,000 =$20,000 = \$25,000 Contribution Margin RATIO 0.80 0.80
Management can also use its knowledge of cost-volume-profit relationships to determine whether to increase sales promotion costs in an effort to increase sales volume or to accept an order at a lower-than-usual price. In general, the careful study of cost behavior helps management plan future courses of action.